Escaping Import Competition in China

Ana Cecılia Fieler, Ann Harrison∗

February 2019

Abstract

We propose and provide evidence for a new source of gain from trade: Firmsdifferentiate their products to escape import competition. Facing a nested CESdemand, heterogeneous firms choose between producing a variety in a nest withcompetitors or incurring a higher cost to be a monopolist in a new nest. The gainfrom differentiation is an inverted U-shaped function of firm productivity, and it islarger for the social planner values than for private firms. We use establishmentdata from China spanning its WTO accession in 2001. In the data, tariff cuts areassociated with increases in revenue productivity, introduction of new goods, andswitches to skill-intensive sectors within firms. These patterns are in line with theprediction that import competition increases product innovation. Variable markupsexplain the effect of tariff cuts on the revenue productivity of firms with heteroge-neous sizes.

∗Fieler: Department of Economics at Yale University and NBER. Harrison: Haas School of Businessat the University of California Berkeley and NBER. We are grateful to Matilde Bombardini, BeataJavorcik, Jonathan Eaton, Teresa Fort, Elisa Giannone, Amit Khandelwal, Andres Rodriguez-Clare,Esteban Rossi-Hansberg, Eric Verhoogen, and Shang-Jin Wei for their suggestions. We also thank theseminar participants at Columbia, MIT, Princeton, Stanford, Toronto, and Zurich. The research for thispaper was conducted in part while Fieler was visiting the Economics Department at Princeton University.We thank them for their hospitality.

1 Introduction

Policy makers and trade economists generally agree that trade reforms improve the perfor-

mance of domestic competitors, even though the theoretical and empirical underpinnings

for this view remain elusive. Evidence on the effect of tariff or quota reductions on firm

productivity is mixed, and if forced to explain a mechanism, a number of economists

might vaguely resort to “x-inefficiency” or “dynamic gains from trade.”1 This paper aims

to, at least in part, narrow the gap between policy makers’ perceptions and the academic

literature.

In response to lower import tariffs, firms often differentiate their products by seek-

ing market niches that are insulated from foreign competition. They cater to domestic

tastes, offer greater customization, and complement products with non-tradable services.

Anecdotes abound from the Chinese accession to the WTO in 2001, the object of our

empirical analysis. Shortly after 2001, the automobile company Chery introduced several

new, small car models with many optional features, and it made replacement parts readily

available. These changes insulate Chery from import competition because it is difficult

for firms producing cars abroad to offer customized accoutrements and a wide range of

replacement parts. Similarly, the cell phone company Xiaomi prevented the expansion

of Apple in China by offering Chinese language options and a superior integration of its

software with local apps.2

We capture this sort of reaction to foreign competition in a model with heterogeneous

firms and a demand system with nested constant elasticity of substitution (CES). Firms

compete a la Bertrand and have endogenous markups. In addition, each firm chooses

between (1) producing a variety in a less-differentiated nest with a high elasticity of sub-

stitution between varieties, and (2) incurring a higher (fixed or variable) cost to produce

in a new nest where it is a monopolist. This choice of product differentiation is our only

departure from the simplest version of Atkeson and Burstein (2008).

In the model, the net profit from product differentiation is a non-monotonic function

of firm productivity. If the firm is very unproductive, its profit is small irrespective of

whether it produces a differentiated variety or not. If the firm is much more productive

1See Holmes and Schmitz (2010) for theories and case studies based on x-inefficiencies. Tybout(2003) surveys of studies on the trade liberalizations in developing countries in the 1980s and 1990s.Mixed evidence appears in more recent papers, e.g., Amiti and Konings (2007), Eslava et al. (2013),DeLoecker et al. (2016) and Steinwender (2015). Our empirical findings do not preclude the presence ofx-inefficiencies, but our mechanisms has specific predictions that are bore out by the data.

2See Farhoomand and Schuetz (2007), Boyd et al. (2008), Teagarden and Fifi (2015), Feng and Wei(2015). In interviews with Foreign Affairs (Rose (2015)), American entrepreneurs emphasize their searchfor market niches where they can enjoy monopoly power.

2

than its competitors, then it will hold near monopoly power and charge a high markup

even in the less-differentiated nest. The benefit from further differentiation is small.

When competition tightens in the less-differentiated nest, the profit from escaping

competition to a new nest increases for all firms. To understand the effects of foreign

competition, we assume that at least some foreign firms are in the less-differentiated nest.

The interpretation is that differentiated goods are less tradable because they cater to

domestic tastes and are complemented with non-tradable services. Then, a reduction

in foreign costs increases product differentiation among import-competing firms, in line

with the anecdotes above. We extend the model to general equilibrium and show that the

private profit from product differentiation is smaller than the social benefit. A greater

product differentiation, spurred by import competition, is a gain from trade not previously

identified in the literature. A back-of-the-envelope calculation in Section 4 shows that such

gain may be sizable.

We seek evidence for the proposed mechanisms in panel data of Chinese firms from

1998 to 2007, spanning the year of China’s accession to the WTO in 2001. Average tariffs

on manufacturing in China fell from 43 percent in 1994 to 9.4 percent in 2004. Imports as

a share of GDP doubled from 14 percent in 1998 to a peak of 28 percent in 2006. In the

data, tariff cuts are associated with increases in revenue productivity, the introduction

of new goods, and switches to more skill-intensive sectors.3 These facts, we argue, are

at odds with existing models of international trade, where import competition decreases

sales and markups. It leads firms to divest in cost-reducing technologies, drop their

least productive varieties, and switch to unskill-intensive sectors in an unskill-abundant

country. (See Section 2.4.)

Greater product differentiation may rationalize these empirical findings. Firms that

differentiate introduce new goods, and often upgrade their quality and switch to skill-

intensive activities. For example, to offer greater variety and customization of car features,

the automobile company Chery invested in research and development, modern machinery,

and integrated computer systems. Some common sector switches in the data include from

cotton and chemical fibers to textile and garments manufacturing, and from steel rolling

processing to metal structures (Section 2.3). They suggest upgrading to higher value-

added sectors with a greater the scope for differentiation.

The advantage of a model with variable markups is that it speaks directly to revenue

productivity, a measure of the ratio of revenue to cost. In the model, this ratio increases

3Tariff cuts increase the probability of switching sectors and of switching to a more skill intensivesector conditional on switching. To establish causality, we follow the literature in using initial tariffs asinstruments for tariff changes. See Goldberg et al. (2009), Amiti and Konings (2007), Attanasio et al.(2004). We cannot observe changes in skill intensity because we only observe skill intensity in one year.

3

with the markup, which in turn increases with product differentiation and decreases with

tighter competition. Tariff cuts lead import-competing firms to differentiate their products

and to decrease their markups for a given level of differentiation. These opposing effects

may explain the mixed findings of the effect of tariff cuts on firm productivity in the

literature. For the Chinese experience, these effects are positive, but small.

We find two instances where the productivity responses to tariff cuts in the data differ

from the responses of the other non-pecuniary firm outcomes—the introduction of new

goods and switches to more skill-intensive sectors—which we use as proxies for product

differentiation. First, the productivity response to tariff cuts decreases systematically

with quartile of sales, while the response of non-pecuniary firm outcomes is the same

across quartiles of sales. In line with this finding, we prove that import competition

increases the markup of small firms relative to large firms if firms of all sizes have similar

propensities to differentiate their products. Second, the productivity response to tariff

cuts is at least seven times larger for import-competing firms’ input suppliers than the

response of import-competing firms themselves. The movement in non-pecuniary firm

outcomes is generally smaller for input suppliers than for import-competing firms. We

extend the model to include input suppliers and show that these firms increase both

differentiation and markups in response to import-competition downstream, again in line

with the data. In sum, predicted changes in markups in the model coincide with observed

changes in revenue productivity in the data, even when these predictions and empirical

regularities are different from those of non-pecuniary firm outcomes. This result suggests

caution in interpreting changes in measured productivity during large trade liberalizations

episodes.4

Holmes and Stevens (2014) also observe that firms offering customized products are

more insulated from foreign competition. We extend their model to account for endoge-

nous product differentiation and variable markups. Consistent with our findings, Brandt

and Thun (2010) and Brandt and Thun (2016) describe the increased market segmentation

in China during the period of our analysis.5

The result that the profit from innovation is an inverted U-shape is reminiscent of

Aghion et al. (2005) and Aghion et al. (2015). In these models, innovation reduces the

cost of producing a homogeneous good, and only the most productive firm produces. Our

4Methods to estimate TFP and to separate it from markups generally assume technology changesare Hicks neutral and goods are homogeneous. These assumptions that are violated by the model andarguably the data as trade changes firms’ residual demand functions, and innovation changes output andproduction processes. See Section 3.1 for discussion and references.

5Fort et al. (2018) associate import penetration in the United States to shifts of manufacturing firmsto the service sector. This finding is also in line with our thesis that firms complement their output withnon-tradable services to escape foreign competition.

4

use of CES preferences with differentiated varieties brings their results closer to recent

quantitative trade models. Starting with Feenstra and Hanson (1997), recent papers pro-

pose theories where international trade leads firms to upgrade their quality or technologies

in unskill-abundant developing countries.6 Upgrades in these theories occur through ex-

port expansion, imported inputs or capital, and we propose import competition as an

additional mechanism.

To our knowledge, the effects of tariff cuts on the input suppliers of import-competing

firms have not been previously documented. These results are part of a growing literature

that highlights the role of domestic input linkages in propagating and augmenting the

direct effects of international trade on firms, such as Kee and Tang (2016), Fieler et al.

(2018), Linarello (2018), and Tintelnot et al. (2018).7 Our results on the welfare effects

of product differentiation complement the results on optimal variety in Dixit and Stiglitz

(1977) and Dhingra and Morrow (2018).

The description of the data, empirical specification, and results are in Section 2. Sec-

tion 3 presents a simple, partial equilibrium model that rationalizes the empirical findings.

Section 4 extends the model to general equilibrium to analyze welfare. Section 5 extends

the model to include intermediate inputs. Appendix A tests other predictions of the

model and checks the robustness of the empirical results. Section 6 summarizes these

data exercises. Section 7 concludes.

2 Data and Evidence

We analyze the effect of tariff changes on firm outcomes that are often associated with

innovation or quality upgrading in the literature: productivity, introduction of new goods,

and skill intensity. We describe the data sources in Section 2.1, the empirical specification

in Section 2.2, and the results in Section 2.3. Given the relevance of Chinese accession

to the WTO, these results are themselves of interest. They motivate the model because

they are hard to reconcile with existing models, as we argue in Section 2.4.

6 This literature is typically concerned with explaining the increased demand for skilled workersfollowing trade liberalizations in developed countries. See Yeaple (2005), Burstein and Vogel (2016),Burstein et al. (2016), Helpman et al. (2017), Fieler et al. (2018), and Lee (2018). Goldberg and Pavcnik(2004) and Goldberg and Pavcnik (2007) survey empirical works.

7Our empirical approach is closely related Javorcik (2004) and Blalock and Gertler (2008) used tostudy spillovers in foreign direct investment. The direct effects of imported inputs are in Amiti andKonings (2007), Goldberg et al. (2010), Halpern et al. (2015), Bøler et al. (2015), and Brandt et al.(2017) for China.

5

2.1 Data Sources

The data are an annual survey of industrial firms collected by the Chinese National

Bureau of Statistics. The survey is at the establishment level and comprises all state-

owned enterprises (SOEs), regardless of size, and all non-state-owned firms (non-SOEs)

with annual sales of more than 5 million yuan. We use a ten-year unbalanced panel from

1998 to 2007. These data are extensively used in a number of papers, and for more details,

we refer the reader to Du et al. (2012), Aghion et al. (2015), and Brandt et al. (2017).

The original dataset has 2,226,104 firm-year observations and contains identifiers that

can be used to track firms over time. We keep only firms in manufacturing, the more

tradable sector. We delete observations with missing values, or with zero or negative

values for output, number of employees, capital, and material inputs. Output price indices

by sector are reported annually in the official publication. We dropped three sectors from

the sample due to missing data on price indices.

The data contain information on output, fixed assets, total workforce, total wages,

intermediate input costs, foreign investment, Hong Kong-Taiwan-Macau investment, sales

revenue, and export sales. We classify firms as domestic or foreign-owned. Domestic firms

are those with zero foreign capital in their total assets. About 77.5 percent of firms are

classified as domestic and 22.5 percent as foreign-owned. Most of our analysis restricts

the sample to domestic firms with zero or a minority state ownership, but we confirm

that our results are robust to including multinationals and state owned enterprises. The

final sample has 1,037,738 observations.

Our time series of tariffs is the World Integrated Trading Solution (WITS), maintained

by the World Bank. To measure tariffs on sectors upstream and downstream from each

firm’s own sector, we use Chinese Input-Output table (2002). The sectoral classification

in the input-output table is more aggregate than the 4-digit classification in the firm

survey. So, we create a concordance between the tariff data, the input-output table, and

the survey data at the most disaggregated level possible. The aggregation uses output

in 2003 as weights. We end up with 71 sectors that comprise a wide range of economic

activities, such as ship-building, electronic computers, tobacco products, motor vehicles,

and parts and accessories for motor vehicles.

6

2.2 Empirical Specification

Our basic regression specification is:

yit =β1 ln Output Tariffj(i,t)t + β2 ln Upstream Tariffj(i,t)t + β3 ln Downstream Tariffj(i,t)t

+ γ1Xj(i,t)t + γ2Xi,t + αi + αt + ε (1)

where the subscripts refer to firm i, year t, and sector j(i, t) of firm i at time t. Variable

yit is an outcome of interest, αi are firm fixed effects, and αt are time fixed effects. Control

variables are at the sector-time level Xjt and at the firm-time level Xit. These controls

and tariff measures are detailed below. We cluster standard errors by firm and by the

firm’s initial sector.

Tariffs For each firm and year, we construct three measures of the tariffs that China

imposes on its imports. Consider a firm in sector j. First, output tariffs are tariffs on

the firm’s own sector j. Second, upstream tariffs are tariffs on the sectors that provide

inputs to sector j. The literature refers to them as input tariffs, and we change the

nomenclature to make it symmetric to the novel concept of downstream tariffs. Third,

downstream tariffs are tariffs on the sectors to which firms in sector j provide inputs.

Consider the example of a firm that produces car engines. It may be impacted by

Chinese entry into the WTO if the tariffs on the pistons that go into engines decrease

(upstream tariff), if the tariffs on car engines decrease (output tariff) increasing import

competition, or if tariffs on cars decrease (downstream tariff) and change the type of car

Chinese producers make.

Output tariffs are measured at the four-digit level, while upstream and downstream

tariffs are measured at the 71-sectoral classification, as described above. Our measure of

upstream tariffs follows Amiti and Konings (2007) and is used by Brandt et al. (2017) for

China.8 Upstream tariff is a weighted average of output tariffs:

upstream tariffjt =∑m 6=j

δjm output tariffmt

where the weight δjm is the share of sector m in all of sector j’s inputs. Downstream tariff

8We take our upstream and output tariffs directly from Brandt et al. (2017), who study China in thesame period with the same data sources.

7

is calculated analogously as:

downstream tariffjt =∑k 6=j

αjk output tariffkt

where αjk is the share of sector j’s production supplied to downstream sector k. The

values of αjk and δjm are both taken from the 2002 Chinese Input-Output table. These

weights αjk and δjm do not add up to one because inputs include labor and capital, and

part of output goes to final consumption. Downstream tariffs will be highest in those

sectors j where the downstream users in sector k face high tariffs and demand a large

share of sector j’s output.

Instruments for tariffs The high level of aggregation at which upstream and down-

stream tariffs are measured, 71 sectors, partly mitigates the concern that individual firms

endogenously influence the level of tariffs through lobbying. Still, we use an instrumental

variable to further address the potential endogeneity of tariffs. Similar to other trade

liberalizations, China reduced both the level and the heterogeneity in tariffs. Between

1998 to 2007, tariff reductions were larger in sectors with high tariffs at the beginning of

the sample period, in 1998.

Following the literature, we use initial tariffs as instruments.9 Output tariffs, upstream

tariffs, and downstream tariffs are instrumented using the initial value for these tariffs

at the firm level interacted with a dummy variable equal to one after China entered the

WTO. We cannot use the initial tariffs alone as an instrument because our regressions

have firm fixed effects.

Additional control variables Control variables capture exposure to foreign invest-

ment and state ownership at the sector-time level, and policy variables at the firm-time

level. We control for the share of state ownership in the sector of the firm at time t.

We define three sector-level FDI variables following Javorcik (2004). Horizontal FDIjt

captures foreign presence in sector j at time t, and it is a weighted average of foreign

equity participation in each firm in sector j, where the weights are the firm’s share in

sectoral output. Downstream FDIjt is a measure of foreign participation in the sectors

that are supplied by sector j, i.e., in sectors downstream from j. Upstream FDIjt is a

measure of foreign participation in sectors upstream from j. We refer the reader to Javor-

9For example, Goldberg et al. (2009) use this instrument for India, Amiti and Konings (2007) useit for Indonesia, and Attanasio et al. (2004) use it for Colombia. Brandt et al. (2017) follow a similarapproach for instrumenting Chinese tariffs. They instrument for tariffs using rates from the accessionagreement, which were mostly fixed by 1999.

8

cik (2004) for details on the construction of these FDI variables. We control for industrial

policy through zero-one dummy variables indicating whether the firm received subsidies

(index subsidies), whether the firm received a tax holiday (index tax), and whether the

firm paid below median interest rates on loans (index interest). Compared to other stud-

ies, our control variables are very detailed, but level of aggregation is high—Amiti and

Konings (2007), for instance, use 4-digit measures of protection for Indonesia, while we

can only use 3-digit measures for tariffs and FDI.

Revenue Total Factor Productivity (TFP) Our main measure of revenue TFP uses

the standard two-stage procedure in Olley and Pakes (1996) to estimate the following

gross-output production function separately for each 2-digit sector:

lnXit = α0j(i,t) + αLj(i,t) lnLit + αMj(i,t) lnMit + αKj(i,t) lnKit + µit (2)

where X is deflated output, L is number of employees, K is capital, M is material inputs,

and α0j, αLj, αKj and αMj are sector-specific parameters to be estimated.10 Our estimated

lnTFPit is the predicted value of lnXit− αLj(i,t) lnLit− αMj(i,t) lnMit− αKj(i,t) lnKit. The

results below are robust to measuring TFP a la Ackerberg et al. (2015) in Appendix A.1.

2.3 Empirical Results

Revenue TFP Table 1 shows the results from regression (1) when the dependent

variable is lnTFPit. The regression includes sector fixed effects due to the concern that

TFP may not be comparable across sectors.11 TFP in (2) is measured either following

Olley-Pakes (OP) or OLS with fixed effects (FE), as indicated in each column.

The coefficients on output tariffs, downstream tariffs, and upstream tariffs in the first

three rows are negative and statistically significant in all specifications: Reductions in

these tariff measures are associated with increases in TFP. The OLS estimates are in

Columns (1) and (2), and we instrument for tariffs (IV) in Columns (3) and (4). The

coefficient on the WTO dummy interacted with initial tariff levels in the first stage is

10All output and input variables are deflated. Output value (quantities*prices) is deflated by the 29individual sector ex-factory price indices of industrial products. To deflate material inputs, these 29sector price indices are assigned with as much consistency as possible to the output data for the 71 sectoraggregates. Capital is defined as the net value of fixed assets, which is deflated by a uniform fixed assetsinvestment index, and labor is a physical measure of the total number of employees. Intermediate inputsused for production are deflated by the intermediate-input price index.

11In Appendix A.1, the results hold also without these sector fixed effects. For the other outcomevariables, we do not include sector fixed effects to capture product innovation that may be accompaniedby firms switching between 4-digit sectors. Similar results appear in Brandt et al. (2017) and Yu (2014).

9

Tab

le1:

Bas

icR

egre

ssio

ns

ofP

roduct

ivit

yon

Tar

iffs

Dep

en

dent

vari

ab

le:

TF

Pm

easu

red

ala

Oll

ey-P

akes

(OP

)or

OL

Sw

ith

fixed

eff

ects

(FE

)

All

Ente

rpri

ses

Excl

ud

ing

SO

Es

an

dM

ult

inati

on

als

On

lyN

on

-Exp

ort

ers

mea

sure

ofT

FP

−→O

PF

EO

PF

EO

PF

EO

LS

OL

SIV

IVIV

IV(1

)(2

)(3

)(4

)(5

)(6

)

outp

ut

tari

ff-0

.0304***

-0.0

322***

-0.0

505***

-0.0

477***

-0.0

617***

-0.0

580***

(0.0

027)

(0.0

028)

(0.0

169)

(0.0

184)

(0.0

158)

(0.0

170)

dow

nst

ream

tari

ff-0

.0179**

-0.0

194**

-0.1

78***

-0.1

73***

-0.4

21***

-0.4

44***

(0.0

070)

(0.0

079)

(0.0

627)

(0.0

641)

(0.0

650)

(0.0

672)

up

srte

amta

riff

-0.1

32***

-0.1

41***

-0.3

69***

-0.4

83***

-0.2

27**

-0.3

23***

(0.0

118)

(0.0

130)

(0.0

975)

(0.1

020)

(0.0

907)

(0.0

938)

ind

exsu

bsi

dy

0.0

106***

0.0

128***

0.0

100***

0.0

120***

0.0

0745***

0.0

0875***

(0.0

012)

(0.0

012)

(0.0

012)

(0.0

012)

(0.0

015)

(0.0

015)

ind

exta

x0.0

216***

0.0

220***

0.0

213***

0.0

217***

0.0

210***

0.0

215***

(0.0

009)

(0.0

009)

(0.0

009)

(0.0

010)

(0.0

010)

(0.0

010)

ind

exin

tere

st-0

.0121***

-0.0

133***

-0.0

119***

-0.0

132***

-0.0

133***

-0.0

144***

(0.0

009)

(0.0

009)

(0.0

009)

(0.0

009)

(0.0

010)

(0.0

010)

exp

orts

har

ese

ctor

0.1

21***

0.1

66***

0.3

98***

0.4

88***

0.4

79***

0.5

78***

(0.0

352)

(0.0

357)

(0.0

513)

(0.0

539)

(0.0

582)

(0.0

615)

Sta

tesh

are

0.0

00537

0.0

012

0.0

00136

0.0

00733

0.0

0176

0.0

0279

(0.0

037)

(0.0

037)

(0.0

037)

(0.0

037)

(0.0

042)

(0.0

043)

Hor

izon

tal

FD

I0.1

45***

0.2

04***

0.1

35***

0.1

87***

0.2

24***

0.2

86***

(0.0

394)

(0.0

420)

(0.0

412)

(0.0

439)

(0.0

487)

(0.0

513)

Dow

nst

ream

FD

I1.1

84***

1.1

08***

1.7

18***

1.6

52***

2.2

81***

2.2

62***

(0.1

940)

(0.2

060)

(0.2

760)

(0.2

890)

(0.2

960)

(0.3

120)

Up

stre

amF

DI

0.0

926

0.1

0.1

56**

0.1

85**

0.0

42

0.0

726

(0.0

724)

(0.0

736)

(0.0

752)

(0.0

764)

(0.0

786)

(0.0

795)

Ob

serv

atio

ns

1,0

37,7

38

1,0

37,7

38

1,0

37,7

38

1,0

37,7

38

826,0

72

826,0

72

Fst

atis

tic,

log(

outp

ut

tari

ff)

=lo

g(d

own

stre

amta

riff

)3.1

2.6

4.3

4.0

31.8

34.3

Fir

stS

tage

F,

outp

ut

tari

ff-

-277.6

277.6

349.8

349.8

Fir

stS

tage

F,

dow

nst

ream

tari

ff-

-630.1

630.1

524.1

524.1

Fir

stS

tage

F,

up

stre

amta

riff

--

142.8

142.8

161.8

161.8

Sta

nd

ard

erro

rsar

ecl

ust

ered

by

firm

and

init

ial

sect

or.

Tari

ffs

an

dT

FP

are

inlo

gs.

All

spec

ifica

tions

incl

ud

efi

xed

effec

tsfo

rth

efi

rm,

tim

e,an

dtw

o-d

igit

sect

or.

All

spec

ifica

tion

sal

soin

clu

de

ad

um

my

vari

ab

leeq

ual

to1

ifth

efirm

chan

ges

afo

ur

dig

itse

ctor.

IVes

tim

ate

su

sein

itia

l1998

tari

ffs

and

init

ial

tari

ffs

inte

ract

edw

ith

aW

TO

du

mm

yas

inst

rum

ents

.∗∗∗

ind

icate

sp<

0.01,∗∗p<

0.0

5,

an

d∗

ind

icate

sp<

0.1.

10

highly significant and negative (F-statistics reported), indicating that China’s entry into

the WTO led to significant tariff declines, especially in manufacturing sectors with high

initial tariffs. For the IV estimates, the coefficient on output tariffs in the OP and FE

productivity measures are respectively -0.0505 and -0.0477. A ten percent reduction in

tariffs raises TFP by about 0.5 percent. Columns (5) and (6) repeat the estimation only

with non-exporting firms. The coefficients above increase in absolute value to -0.0617 and

-0.0580, respectively, suggesting that import competition has a positive effect on TFP

beyond firms’ participation in global value chains and export markets.

New goods We use two measures of the introduction of new goods as the dependent

variable in regression (1). First is the share of new products in total sales, as reported in

the survey. Second is a dummy variable equal to one if the firm introduces a new product

in a particular year and zero otherwise.

The results are in Table 2. In all specifications, the coefficient on output tariffs is

negative indicating that import-competing firms introduce new goods in response to tariff

cuts. For example in the IV columns (2) and (4), the coefficients indicate that a one stan-

dard deviation reduction in log output tariffs, around 0.5, is associated with an increase

of 0.8 percentage points in the share of new products in total sales (0.5 multiplied by

-0.0157), and with an increase of 2 percentage points in the probability of introducing a

new product (0.5 multiplied by -0.0405). The coefficient is also negative when we restrict

the sample only to non-exporting enterprises in columns (5) and (6).12

Skill Intensity A commonly used indicator of firm quality is skill intensity. Unfortu-

nately, we only observe details on the composition of the work force in the 2004 survey.

We use this 2004 cross-section to measure sectoral skill intensity and then test whether

tariff cuts prompted firms to switch to skill-intensive sectors.

We define skilled workers as those who have completed a senior-high degree, or a three-

or four-year college degree.13 We calculate the share of skilled workers in the total labor

force of each sector in 2004 and rank sectors according to skill intensity. There are 450

sectors in the data. The least skill-intensive sector is the production of packaging and

bags, and the most skill intensive sector is a subsector in aircraft manufacturing.

Table 3 presents the results from regression (1) where the dependent variable is sec-

toral rank, with highest indicating most skill-intensive. The first two columns report

12The coefficients in the OLS specifications are all small and statistically insignificant. This result mayoccur if firms introduce new goods in response to the large tariff cuts of the WTO accession but not tosmaller tariff cuts in other years.

13Changing the educational cutoffs in the definition of skill intensity yields highly correlated measures.

11

Tab

le2:

Intr

oduct

ion

ofN

ewG

oods

All

ente

rpri

ses,

excl

ud

ing

SO

Es

an

dM

ult

inati

onals

On

lyN

on

-Exp

ort

ers

dep

end

ent

vari

able→

new

new

0-1

du

mm

yfo

r0-1

du

mm

yfo

rn

ew0-1

du

mm

yfo

rp

rod

uct

pro

du

ctin

trod

uci

ng

intr

od

uci

ng

pro

du

ctin

trod

uci

ng

share

share

an

ewa

new

share

an

ewp

rod

uct

pro

du

ctp

rod

uct

OL

SIV

OL

SIV

IVIV

(1)

(2)

(3)

(4)

(5)

(6)

outp

ut

tari

ff-0

.000356

-0.0

157**

-0.0

00687

-0.0

405**

-0.0

0976**

-0.0

279***

(0.0

012)

(0.0

068)

(0.0

029)

(0.0

168)

(0.0

045)

(0.0

102)

dow

nst

ream

tari

ff-0

.00372

-0.0

272

0.0

0777

-0.0

533

-0.0

313**

-0.0

423

(0.0

024)

(0.0

184)

(0.0

078)

(0.0

399)

(0.0

147)

(0.0

266)

up

srte

amta

riff

0.0

0251

0.0

33

-0.0

016

0.1

03*

0.0

404**

0.0

893**

(0.0

037)

(0.0

274)

(0.0

092)

(0.0

622)

(0.0

186)

(0.0

382)

ind

exsu

bsi

dy

0.00631***

0.0

0635***

0.0

170***

0.0

171***

0.0

0449***

0.0

116***

(0.0

008)

(0.0

008)

(0.0

016)

(0.0

016)

(0.0

008)

(0.0

014)

ind

exta

x-0

.000694*

-0.0

00663*

-0.0

0213**

-0.0

0204**

-0.0

00451

-0.0

0145**

(0.0

004)

(0.0

004)

(0.0

009)

(0.0

009)

(0.0

004)

(0.0

007)

ind

exin

tere

st-0

.00183***

-0.0

0177***

-0.0

0617***

-0.0

0600***

-0.0

00943**

-0.0

0347***

(0.0

004)

(0.0

004)

(0.0

010)

(0.0

010)

(0.0

004)

(0.0

008)

exp

orts

har

ese

ctor

-0.0

128

0.0

0461

-0.0

0328

0.0

322

-0.0

0341

-0.0

189

(0.0

10)

(0.0

13)

(0.0

25)

(0.0

29)

(0.0

11)

(0.0

23)

Sta

tesh

are

0.0

00525

0.0

00416

0.0

0616*

0.0

0597

0.0

00107

0.0

0287

(0.0

020)

(0.0

020)

(0.0

037)

(0.0

037)

(0.0

021)

(0.0

036)

Hor

izon

tal

FD

I0.

0314***

0.0

229*

0.0

249

-0.0

0632

0.0

227**

0.0

237

(0.0

11)

(0.0

14)

(0.0

27)

(0.0

34)

(0.0

11)

(0.0

23)

Dow

nst

ream

FD

I-0

.00932

0.0

266

-0.0

532

0.0

261

0.0

454

0.0

152

(0.0

24)

(0.0

39)

(0.0

58)

(0.0

86)

(0.0

33)

(0.0

60)

Up

stre

amF

DI

-0.0

0705

-0.0

285**

-0.0

175

-0.0

706***

-0.0

272***

-0.0

540***

(0.0

06)

(0.0

11)

(0.0

13)

(0.0

25)

(0.0

09)

(0.0

18)

Ob

serv

atio

ns

1,037,7

38

1,0

37,7

38

1,0

37,7

38

1,0

37,7

38

826,0

72

826,0

72

Fst

atis

tic,

log(

outp

ut

tari

ff)

=lo

g(d

ownst

ream

tari

ff)

1.7

0.5

1.1

0.1

2.6

0.4

Fir

stS

tage

F,

outp

ut

tari

ff-

340.7

-340.7

447.8

447.8

Fir

stS

tage

F,

dow

nst

ream

tari

ff-

631.1

-631.1

469.4

469.4

Fir

stS

tage

F,

up

stre

amta

riff

-192.6

-192.6

220.3

220.3

Sta

nd

ard

erro

rsar

ecl

ust

ered

by

firm

and

init

ialse

ctor.

All

spec

ifica

tion

sin

clu

de

firm

fixed

effec

tsan

dti

me

effec

ts.

Inst

rum

ents

inth

eIV

spec

ifica

tion

sfo

rlo

gof

outp

ut

tari

ff,

dow

nst

ream

tari

ff,

and

up

stre

am

tari

ffin

clu

de

the

WT

Od

um

my

inte

ract

edw

ith

the

init

ial

tari

ff.∗∗∗

ind

icate

sp<

0.01,∗∗

p<

0.05

,an

d∗

ind

icat

esp<

0.1

.

12

Table 3: Movements to Sectors with Higher Skilled Worker Share Based on 2004 survey

Dependent variable: Ranking of sector according to skill intensity

All Enterprises, Excluding Only Non-ExportersSOEs and Multinationals

OLS IV OLS IV(1) (2) (3) (4)

output tariff -17.82*** -26.20*** -18.80*** -19.27***(1.00) (3.81) (0.89) (3.14)

downstream tariff 6.914*** -33.44*** 5.907*** -31.39***(1.34) (7.40) (1.31) (7.49)

upsrteam tariff 34.04*** 108.5*** 36.85*** 93.35***(2.79) (14.39) (2.75) (13.07)

index subsidy 0.630*** 0.703*** 0.843*** 0.877***(0.16) (0.18) (0.19) (0.20)

index tax 0.134 0.153 0.216** 0.173*(0.09) (0.10) (0.10) (0.10)

index interest -0.390*** -0.338*** -0.431*** -0.428***(0.110) (0.115) (0.123) (0.127)

exportshare sector -194.7*** -185.5*** -209.2*** -202.1***(8.64) (7.80) (7.81) (7.98)

State share -0.194 -0.0456 -0.423 -0.207(0.420) (0.424) (0.467) (0.468)

Horizontal FDI 68.07*** 44.12*** 73.68*** 55.40***(7.60) (9.77) (7.54) (9.29)

Downstream FDI 539.2*** 592.5*** 549.8*** 593.3***(23.83) (27.49) (26.15) (29.35)

Upstream FDI -33.38*** -46.95*** -43.23*** -51.02***(5.58) (6.24) (5.89) (6.51)

Observations 1,037,738 1,037,738 826,072 826,072

F statistic log(output tariff)= log(downstream tariff) 216 1 228 3

First Stage F, output tariff - 341 - 448First Stage F, downstream tariff - 631 - 469First Stage F, upstream tariff - 193 - 220

Sectors with a higher rank (number) are more skill intensive. Standard errors are clustered by firm and

initial sector. All regressions include firm fixed effects and time fixed effects.

13

coefficients for all firms, and the last two columns include only non-exporting firms. Since

all specifications include firm fixed effects, the identification stems from firms switching

sectors. Approximately 15 percent of firms in the sample change sectoral affiliation over

the period from 1998 to 2007.

The coefficient on output tariffs is consistently negative and significant. A decline in

output tariffs is thus associated with a movement to skill-intensive sectors. The point

estimates, ranging from -18 to -26, imply that a one standard deviation reduction in log

tariffs (around .5) is associated with a movement up the rank that ranges between 9 and

13 sectors. Among non-exporting firms, the sector switches with the largest number of

firms include switches from cotton and chemical fibers (1761) to textile and garments

manufacturing (1810), and from steel rolling processing (3230) to the manufacture of

metal structures (3411), from non-ferrous rolling process (3351) to optical fiber and cable

manufacturing (3931). In all cases, these switches are from lower value-added products or

stages of production to higher value-added products, where the scope for differentiation

is arguably greater. They are thus consistent with our thesis that firms escape import

competition by differentiating their products.

Firm Heterogeneity Table 4 investigates whether the responses to tariff cuts differ

across firms of different sizes. We split firms in each sector-year into quartiles of sales, and

we repeat regression (1) replacing the main independent variable of interest output tariff

with output tariff interacted with dummies of whether the firm is in quartile q = 1, ..., 4

of sales within its sector-year. The dependent variables are TFP, introduction of new

goods, and the ranking of skill-intensive sectors as in Tables 1, 2, and 3.

Table 4 reports only the coefficients of interest.14 The dependent variable in Panel

B measures the introduction of new goods, and in Panel C, it is the ranking of sectoral

skill-intensity. In all specifications of Panels B and C, the coefficients on output tariffs

are very similar across quartiles of firm sales. In contrast in Panel A where the dependent

variable is TFP, the coefficient on output tariffs increases systematically with quartile of

sales, and the differences are statistically significant. In response to tariff cuts, the TFP

of small firms increases while the TFP of large firms decreases.

Downstream Tariffs In all IV specifications, the coefficient on downstream tariffs in

Tables 1, 2 and 3 are negative and equality with the coefficient on output tariffs cannot

be rejected. In the OLS specification, the coefficient on downstream tariffs is generally

14See Appendix A.4 for other coefficients. The coefficients on the other two tariff measures practicallydo not change from Tables 1, 2, and 3.

14

Table 4: Heterogeneous responses of firms to output tariff cuts

Panel A: Dependent variable is TFP a la Olley-Pakes or OLS with fixed effects (FE)

All firms excluding SOEs and multinationals Only non-exportersOP FE OP FE OP FEOLS OLS IV IV IV IV

output tariff*q1 -0.108*** -0.112*** -0.0975*** -0.0966*** -0.115*** -0.114***(0.00279) (0.00291) (0.0162) (0.0174) (0.0147) (0.0154)

output tariff*q2 -0.0607*** -0.0639*** -0.0408** -0.0377** -0.0554*** -0.0515***(0.00266) (0.00278) (0.0161) (0.0173) (0.0146) (0.0153)

output tariff*q3 -0.0159*** -0.0173*** 0.0187 0.0245 0.00770 0.0146(0.00259) (0.00271) (0.0160) (0.0172) (0.0145) (0.0152)

output tariff*q4 0.0385*** 0.0398*** 0.0950*** 0.105*** 0.0871*** 0.0982***(largest) (0.00261) (0.00273) (0.0161) (0.0173) (0.0145) (0.0153)

Observations 1,037,738 1,037,738 1,037,738 1,037,738 826,072 826,072(panels A, B, C)

Panel B: Dependent variable is a measure of introduction of new goods

All firms excluding SOEs and multinationals Only non-exportersdependent variable → new 0-1 dummy new 0-1 dummy new 0-1 dummy

product for new product for new product for newshare product share product share productOLS OLS IV IV IV IV

output tariff*q1 -0.000914 -0.00566** -0.0160** -0.0438*** -0.0103** -0.0300***(0.00119) (0.00287) (0.00679) (0.0167) (0.00447) (0.0102)

output tariff*q2 -0.000700 -0.00262 -0.0156** -0.0396** -0.00966** -0.0276***(0.00121) (0.00290) (0.00677) (0.0167) (0.00445) (0.0101)

output tariff*q3 -0.000557 -0.000705 -0.0153** -0.0369** -0.00940** -0.0261***(0.00122) (0.00292) (0.00675) (0.0167) (0.00442) (0.0101)

output tariff*q4 0.000522 0.00446 -0.0138** -0.0301* -0.00895** -0.0227**(largest) (0.00123) (0.00298) (0.00672) (0.0167) (0.00445) (0.0101)

Panel C: Dependent variable is the sector ranking in skill intensity(higher ranking corresponds to greater skill intensity)

All firms excluding SOEs and multinationals Only non-exportersOLS IV OLS IV

output tariff*q1 -7.631*** -12.40*** -8.445*** -10.50***(0.854) (2.532) (0.778) (1.970)

output tariff*q2 -7.582*** -12.33*** -8.375*** -10.41***(0.856) (2.526) (0.781) (1.966)

output tariff*q3 -7.650*** -12.29*** -8.435*** -10.39***(0.864) (2.531) (0.788) (1.968)

output tariff*q4 -7.561*** -12.04*** -8.340*** -10.18***(largest) (0.864) (2.531) (0.788) (1.967)

The table repeats the results of Table 1 through 3, substituting the independent variable output tarifffor an interaction of output tariff with a dummy indicating the firm’s quartile of sales in period t−1 (q1,q2, q3, q4). Only the coefficients on the interaction terms are reported, but the regressions include thesame other independent variables as the previous tables. Appendix A.4 reports the coefficients on theother control variables.

15

statistically insignificant and at times flips sign. These results suggest that, in response

to tariff cuts, the suppliers of inputs to import-competing firms introduce new goods and

switch to skill-intensive sectors, though plausibly to a smaller extent than the import-

competing firms, directly hit with the shock.

In contrast, when the dependent variable is TFP in Table 1, the coefficients on down-

stream tariffs are about seven times larger than the coefficients on output tariffs in all

IV specifications. This result is robust to numerous checks in Section 6, and Section 5

introduces intermediate inputs to the model to explain it.15

2.4 Empirical Findings and Existing Models

Tables 1, 2, and 3 above suggest that tariff cuts lead import-competing firms to increase

revenue TFP, introduce new goods, and shift toward skill-intensive activities. These

results are broadly in line with the prevailing view among policy makers that import

competition enhances firm performance, but they are difficult to reconcile with existing

models of international trade.

In a large class of models in international trade, firms endogenously invest in higher

technologies when their sales increase, e.g., Bustos (2011), Caliendo and Rossi-Hansberg

(2012), Helpman et al. (2017). In these models, import competition decreases sales and

investments in technologies among non-exporting firms. In contrast in the data, import

competition increases TFP (Table 1) within firms, especially among non-exporting firms.16

Similarly, in trade models with variable markups, such as Bernard et al. (2003), Melitz

and Ottaviano (2008), Atkeson and Burstein (2008), import competition decreases sales

and markups within firms. In all these models, import competition may increase average

productivity or markups through selection, the exit of the least productive firms, but our

regression specification, with firm fixed effects, captures within-firm changes.

The introduction of new goods challenges recent models of multiproduct firms, such

as Bernard et al. (2011) and Mayer et al. (2014). In these models, firms respond to

tighter competition by dropping their least productive varieties, not introducing new ones.

15Differences between TFP and other outcomes appear also in the coefficients on upstream tariffs. Thelarge response of TFP to upstream tariffs could be due to increases in markups as in DeLoecker et al.(2016). Still, the Chinese government has many programs to reimburse input tariffs, and so our upstreamtariff measure may not capture the actual trade barriers faced by firms importing inputs. This point mayexplain the unexpected sign of the coefficient on upstream tariffs in Tables 2 and 3. See Brandt et al.(2017) for similar points on measuring upstream tariffs in China.

16Appendix A.3 analyzes the relation between revenue and TFP. As in other data sets, Table A.11confirms that TFP and revenue are correlated, even after controlling for time and sector fixed effects.And Table A.12 confirms that tariff cuts are associated with decreases in sales. These patterns areconsistent with the models above.

16

Although the classic Heckscher-Ohlin model predicts that trade shifts production across

sectors, it predicts shifts toward unskill-intensive sectors in an unskill-abundant country

like China, the opposite direction of the shifts in Table 3. Recent models predict that trade

may increase the demand for skills even in developing countries.17 These models operate

through export expansion or imported inputs and capital. But our empirical results

exploit variations in tariffs imposed by China, and they hold even when the sample is

restricted to non-exporters, suggesting that import competition also plays a role.

We interpret the findings on new goods and shifts to skill-intensive sectors as evidence

that firms engage in product innovation in response to import-competition. Section 3

presents a simple model where import competition increases product innovation. Al-

though it would be simple to add skills to the model, we do not add it to keep the focus

on innovation. To address TFP results, a measure of the ratio of revenue to cost (equation

(2)), we base our setup on a model of variable markups, Atkeson and Burstein (2008).

3 Theory

The empirical results above pertain to import competition and exploit cross-sectoral vari-

ation. Accordingly, we analyze the behavior of non-exporting firms in partial equilibrium.

There is a continuum of sectors, and we study a fixed and finite set of firms in one sector.

Section 4 extends the set up to general equilibrium.

Firms with heterogeneous productivities compete a la Bertrand. Each firm has a

unique variety. It may exit or pay a fixed cost to produce. If the firm produces, it

chooses between two levels of differentiation. Less-differentiated varieties face a higher

price elasticity of demand but have lower (fixed or variable) costs than more differentiated

varieties. To avoid cumbersome language, we refer to more-differentiated varieties as

“differentiated,” even though the elasticity of demand is finite for all varieties. This

choice of differentiation is the only departure from the simplest version of Atkeson and

Burstein (2008). To highlight it, we initially do not distinguish between domestic and

foreign firms. Foreign firms are introduced in Section 3.2. All proofs are in Appendix B.

17See Feenstra and Hanson (1997), Yeaple (2005), Burstein and Vogel (2016), Burstein et al. (2016),Helpman et al. (2017), Lee (2018), and Fieler et al. (2018).

17

Demand Spending on a variety with price p in nest n follows a nested CES demand

system:

x(p) = Pη−1

P σ−ηn p1−σy (3)

where Pn =

[∑i∈n

p1−σi

] 11−σ

(4)

P =

[∫NP 1−ηn dn

] 11−η

, (5)

y is consumer spending, Pn is the price index of nest n, N is the set of nests, and P is

the overall price index. The elasticity of substitution is η between nests and σ between

varieties within a nest, where σ > η > 1.

There are two types of nests. Nest O contains all less-differentiated varieties. When

a firm has a differentiated variety, it is the single producer in its own nest. Then, Pn = p

and demand reduces to x = (p/P )1−η. Subscript 0 refers to less-differentiated varieties

and D refers to differentiated varieties. There is a continuum of nests. We take y, N ,

and P as exogenous since a finite set of firms cannot affect them. They are determined

in general equilibrium in Section 4.

Technology If the firm exits, its profit is zero. Production requires a fixed cost f0 if

the firm is less differentiated and fD if the firm is differentiated. Firm i’s unit cost is ci0

if the firm is not differentiated and ciD if the firm is differentiated. As in Melitz (2003),

unit costs are adjusted for quality and the model has no predictions for quantity TFP.

Product differentiation is a nontrivial decision for firm i if ciD > ci0 or fD > f0 (or both).

Equilibrium There is an exogenous set of potentially active firms, each with its unit

costs (ci0, ciD).18 In ascending order of cost ci0, each firm decides among three discrete

choices: (i) To exit, (ii) to produce a less differentiated variety, or (iii) to produce a

differentiated variety. Once all discrete choices are made, firms simultaneously set prices.

We consider the subgame perfect equilibrium.19

18One can think of this assumption as allowing for free entry and firm knowledge about their produc-tivity prior to entry. Appendix D.2 introduces free entry to the general equilibrium model.

19The timing of firms’ discrete choices according to productivity is a standard equilibrium selectionmechanism, in Atkeson and Burstein (2008), Edmond et al. (2015).

18

3.1 Equilibrium Characteristics

The equilibrium is solved by backward induction. Consider first the price decisions and

payoffs after all discrete choices are made. Firm i in nest n with unit cost ci chooses price

p to maximize operating profit

π = maxpPη−1

P σ−ηn p−σ(p− ci)y (6)

subject to Pn =

( ∑i′∈n,i′ 6=i

p1−σi′ + p1−σ

)1/(1−σ)

.

The firm best responds to the prices of other firms in its nest. Following Atkeson and

Burstein (2008), the markup over marginal cost is ε/(ε− 1) where

ε = σ(1− s) + ηs, (7)

s =

(p

Pn

)1−σ

The endogenous elasticity of demand ε is a weighted average between the elasticity in the

nest σ and the elasticity across nests η, where the weight s is the market share of the firm

measured in revenue. If the variety is differentiated, Pn = p, s = 1 and demand elasticity

is η. Given a vector of unit costs in the less-differentiated nest {ci0}i∈O, equation (7)

implicitly defines the price for each firm in O. Denote with ε0(c−i0, ci0) the equilibrium

elasticity of demand of a less-differentiated firm with unit cost ci0 when the vector of its

competitors’ costs is c−i0, and P0(c0) as the equilibrium price index in (3) where c0 is the

vector of unit costs in nest O.

Using this pricing rule and unit costs, the operating profit of firm i with and without

product differentiation is, respectively, (equation (6))

πD(ciD) =Pη−1

η

(ηciDη − 1

)1−η

y,

π0(c−i0, ci0) = Pη−1 [P0(c0)]

σ−η

ε0(c−i0, ci0)

([ε0(c−i0, ci0)]ci0ε0(c−i0, ci0)− 1

)1−σ

y. (8)

The profit with differentiation depends only on the firm’s own unit cost ciD. The profit

without differentiation also depends on the vector of unit costs of the firm’s competitors

in the less-differentiated nest, c−i0, through P0 and ε0.

Order the m firms so that c10 < c20 < ... < cm0. Denote an action of firm i with gi ∈{exit, less differentiation, differentiation}. A vector of actions G = (g1, ..., gm) determines

19

the sets of exiting, less-differentiated, and differentiated firms. The payoffs for any G are in

(8). The full game can be solved by backward induction starting with the least productive

firm m and moving up the game tree. For each i = m, ..., 1 and all possible set of actions

(g1, ..., gi−1), firm i chooses among three subgames with starting nodes (g1, ..., gi−1, gi) for

gi = exit, less differentiation, differentiation. These decisions are unique in every node of

the game tree up to a perturbation of parameters. So, the subgame perfect equilibrium is

also unique up to a perturbation of parameters. Throughout, we ignore these indifference

cases and cases in which two or more firms have the same unit cost ci0 or ciD.

Proposition 1 Exit. Suppose that firms can be ranked in terms of costs, ciD < ci′D

if and only if ci0 < ci′0. Then, there exists c > 0 such that firms produce if and only if

ci0 ≤ c. Cutoff c is increasing in P .

Although the decision to exit seems standard, the proof in Appendix B hinges on the

assumption that more productive firms make their discrete choices first. Otherwise, the

entry of a less-productive firm could drive down the price index sufficiently to prevent the

entry of a more productive firm.

A firm’s decision to differentiate its product, in turn, is generally not monotonic in

costs. Proposition 2 characterizes it as a function of its productivity and the competition

it faces in a subgame, captured by c−i0. For the subgame perfect equilibrium, the relevant

vector of competitors’ costs, denoted with c−i0, is the one in the outcome of the subgame

starting with {g1, ..., gi−1, less differentiation}, where gi′ denotes the action of firm i′ in

the equilibrium path.

Proposition 2 Product differentiation. Fix c−i0 and the ratio of unit costs ciD/ci0.

If the set of firm productivity parameters φi ≡ (ci0)−1 such that firm i differentiates its

product is non-empty, then (i) it is a line segment [φ, φ] if differentiation increases unit

costs cDi/c0i ≥ 1, and (ii) it is unbounded if differentiation decreases unit costs cDi/c0i < 1.

The gross gain from product differentiation πD(ciD)− π0(c−i0, ci0) strictly increases if

c−i0 decreases or if c−i0 is augmented with new elements (competitors).

To isolate the novel gain of product differentiation from changes in unit costs, consider

the special case ciD = ci0 ≡ ci. We show that the net gain from differentiation, πD(ci)−π0(c−i0, ci), tends to zero as the firm’s own cost ci tends to zero or infinity. From equation

(8), limci→∞ π0(c−i0, ci) = limci→∞ πD(ci) = 0. For the other limit, let piD = ηci/(η − 1)

be the price of the differentiated variety, and P−i0 be the CES price index in nest O

20

excluding firm i for the given (c−i0, ci).20 Then

πD(ci) =yP

η−1

ηp1−ηiD

≤ yPη−1

η

(P 1−σ−i0 + p1−σiD

)σ−η1−σ P 1−σ

−i0 +yP

η−1

η

(P 1−σ−i0 + p1−σiD

)σ−η1−σ p1−σiD

≤ yPη−1

η

(P 1−σ−i0 + p1−σiD

)σ−η1−σ P 1−σ

−i0 + π0(c−i0, ci)

In the second line is the operating profit of a hypothetical, differentiated firm that charges[P 1−σ−i0 + p1−σD

] 11−σ ≤ piD and gets a share 1/η of revenue as profits. The third line comes

from profit maximization of the less-differentiated firm. Both inequalities hold strictly if

P−i0 <∞. Rearranging and taking limits,

limci→0

[πD(ci)− π0(c−i0, ci)] ≤ limpiD→0

yPη−1

η

(P 1−σ−i0 + p1−σiD

)σ−η1−σ P 1−σ

−i0 = 0

In words, without unit cost changes, ci0 = ciD, the gain in operating profit from differ-

entiation is bounded above by the profit of acquiring the residual demand of competitors

in nest O. Since this residual demand goes to zero as the firm’s own cost ci goes to zero,

the gain from differentiation also goes to zero.21

Figure 1 illustrates the gain from product differentiation net of fixed costs (panel A)

and markups (panel B) as a function of the inverse of the firm’s unit cost when ciD = ci0

and fD > f0, for a given c−i0. If the firm is sufficiently unproductive, then the firm does

not differentiate its product because sales are too small to recoup fixed cost (fD − f0).If the firm is much more productive than its competitors, it practically has a monopoly

in nest O and does not have an incentive to pay a fixed cost to further differentiate its

product. This result is consistent with the case studies surveyed by Holmes and Schmitz

(2010), where monopolists charge high prices for inferior products, and with evidence of

a non-monotonic effect of productivity on innovation in Aghion et al. (2005), Aghion and

20

P−i0 =

∑i′ 6=i,i′∈O

p1−σi′

11−σ

where prices pi′ are implicitly defined in (7) when the productivity vector in O is (c−i0, ci).21The claim limci→0(πD − π0) = 0 is trivial in the limit when σ = ∞ and goods are homogeneous

within nest O as in Bernard et al. (2003). Then, the price is the minimum between the second lowestcost or the monopoly price piD = ηci/(η − 1). For sufficiently high productivity, the firm’s profit in nestO is constant and equal to the case where it differentiates its product. We thank Samuel Kortum forpointing out this case.

21

Figure 1: Gains from product differentiation and markups when ciD = ci0 = ci

Griffith (2008), and Spearot (2013).22

The last statement of Proposition 2 formalizes the effect of escaping competition. For

any ciD and ci0, the gains from product differentiation increases when c−i0 decreases or

is augmented with new elements. In Appendix D1, this result holds when the fixed cost

of creating new nests depends on the number of existing nests because it is increasingly

difficult to find new market ideas, and it holds when there is imitation if the shock to

competition is sufficiently large.

22It is difficult to measure this non-monotonicity in the cross-section of our data, without directlyobserving product differentiation. Table 4 does not present evidence of a non-monotonic response toimport competition. As discussed below, this finding does not necessarily contradict the model.

22

3.2 Foreign Firms

To interpret the empirical results from Section 2, we introduce foreign firms to the model.

In the definition of the equilibrium above, assume that a subset of firms, foreign firms, do

not make discrete choices. They have pre-assigned nests and only enter the final stage of

the game in which prices are set. Their unit costs are exogenous and known, and at least

some foreign firms are in the less-differentiated nest O.

The key underlying assumption is that shocks to foreign costs disproportionately affect

the profit of less-differentiated domestic firms. This assumption appears counterintuitive

in our empirical application to China, a developing country importing goods mostly from

developed countries. But following the anecdotes of Chery and Xiaomi in the introduction,

domestic firms differentiate their products by bundling them with non-tradable services,

catering to domestic tastes, and offering greater customization. The equilibrium is unal-

tered by the existence of a finite set of differentiated foreign firms, i.e., of market niches

with only foreign firms, such as luxuries or high-tech goods. And allowing foreign firms

to exit does not affect the results below, which refer to large decreases in foreign costs.

Propositions 3 and 4 below analyze how the subgame perfect equilibrium changes

when we shock the economy with a decrease in foreign costs. Such a decrease may occur

through the cost of individual varieties or an expansion of varieties. The shock has to be

sufficiently large for competition to tighten in the differentiated nest for all firms, i.e., for

the subgame perfect equilibrium P−i0(c−i0, ci0) to decrease for all i. A large shock satisfies

this condition because, in any subgame and for any firm i, P−i0(c−i0, ci0) is smaller than

the price index P0 in the subgame without domestic firms in nest O.

Proposition 3 Import competition. A sufficiently large decrease in foreign costs

increases exit and product differentiation among surviving firms. The markup increases

for firms that differentiate their products, and it decreases for other firms.

Proposition 3 follows from Proposition 2 and from the price equation (7).23 Figure 2

illustrates effect of the shock when ci0 = ciD and f0 < fD. The solid black curves are the

same as in Figure 1, and the dashed red line indicates the equilibrium after the shock.

In Figure 2A, the gain from differentiation increases because the shock decreases profit

23To see why the statement of the proposition breaks down for small decreases in foreign costs, consideran example with two firms. Before the liberalization, the more productive firm differentiates because itcannot deter the entry of the second firm into nest O if it does not differentiate. As foreign prices decrease,the first firm may choose not to differentiate because it deters the entry of the second firm into nest O.Then, firm 1 shifts from a differentiated to a less-differentiated variety contrary to the proposition. Inthis example, however, the decrease in foreign cost is not sufficiently large. Price index P−10(c−10, c10)increases as firm 2 leaves nest O, either by not producing or differentiating.

23

Figure 2: Effect of import competition on differentiation and markups when ciD = ci0 = ci

π0 and has no effect on πD. In Figure 2B, the markup increases to η/(η − 1) for newly

differentiated firms, and it decreases for firms that remain less-differentiated.

The shock to the Chinese market during the period of its WTO accession was large.

Imports as a share of GDP in China rose from 14 percent in 1998 to 28 percent in

2006. Tables 2 and 3 suggest that, in response to tariff cuts, Chinese firms introduce new

varieties and switch to more skill-intensive sectors. We interpret these results as evidence

of increases product differentiation. The introduction of new varieties is a natural proxy

for differentiation. Some of the most common sectoral switches in the data are to sectors

with a greater scope for differentiation, e.g., from cotton and chemical fibers to textile

and garments manufacturing, and from steel rolling processing to metal structures. In

addition, product differentiation may increase skill-intensive activities within firms even

in a developing country like China. To offer greater variety and customization of car

features, for example, Chery Automobile invested in research and development, and in

24

skill-biased technologies such as modern machinery and integrated computer systems.

The cell phone company Xiaomi designed new software for Chinese usage. While many of

these task changes occur within sectors, some may imply a switch in the firm’s four-digit

sectoral classification.

According to Proposition 3, import competition has an ambiguous effect on markups,

even though it unambiguously increases differentiation among import-competing firms. In

our data, output tariff cuts are associated with increases in revenue TFP (Table 1), but

markups may explain the mixed evidence of the effects of tariff cuts on firm productivity

in the literature despite the commonplace view that trade improves the performance of

import-competing firms.24

Proposition 4 Heterogeneous firms Consider the effect of a sufficiently large decrease

in the cost of foreign varieties on two domestic firms, a and b, originally producing less-

differentiated varieties with ca0 < cb0. If both firms a and b differentiate their products

in response to the shock, the markup increase is larger for firm b than firm a. If both

firms remain less-differentiated, the percentage decrease in firm b’s markup is smaller (in

absolute value) than firm a’s.

Within the same nest, markups are decreasing in firms’ costs. Since the markups of firms

a and b increase to η/(η− 1) if they both differentiate their products, the markup change

is larger for the higher-cost firm. The proof of the case in which both firms remain less-

differentiated is in Appendix B, and it takes into account that firms a and b experience

the original shock differently because they best respond to each other’s markups. We only

note that small firms have little scope for decreasing markups that are already close to

the lower bound σ/(σ − 1).

Proposition 4 refers to heterogeneous firms. The model has no sharp predictions

regarding the size of firms that should differentiate when import competition tightens.

Figure 2 holds in the special case ci0 = ciD and fD > f0, for a given c−i0. In response

to import competition in the model, a large firm that loses its monopoly of the less-

differentiated nest may differentiate its output as well as a small firm if differentiation

does not require large fixed costs, ciD > ci0 and fD ≈ f0. In addition, Appendix B shows

that the set of firms differentiating their products in equilibrium need not be convex in

unit costs even when ci0 = ciD for all firms i, since c−i0 is firm specific.

Proposition 4 predicts that, when foreign costs fall, the markups of large, low-cost

firms decrease relative to smaller firms’ markups if these firms react similarly in terms

of product differentiation. It is relevant because, in Panels B and C of Table 4, firms in

24See references in footnote 1.

25

all quartile of sales have a similar propensity to introduce new goods or switch to skill-

intensive sectors in response to tariff cuts. If we again take these variables as proxies

for differentiation, then the model predicts that the coefficient on output tariffs should

increase systematically with quartile of firm sales when the dependent variable is TFP,

an estimate of the ratio of revenue to cost. Table 4A confirms this prediction.25

Our empirical results on revenue TFP are suggestive but cannot be taken as evi-

dence for the model, because the model violates the assumptions underpinning measures

of productivity and markups in the literature. Assumptions of a Markov path for pro-

ductivity, Hicks neutrality, and product homogeneity are all violated in the model and

arguably in the data as import competition reshapes firms’ residual demand and innova-

tion changes output and production processes. Still, the coincidence between our predic-

tions on markups and movements in measured productivity in the data, even when these

predictions differ from movements in other firm outcomes, suggests caution in interpret-

ing productivity measures and other pecuniary firm outcomes during trade liberalization

episodes.26 We used the introduction of new goods and sectoral-switching as more direct

proxies for differentiation.

4 General Equilibrium and Welfare

The partial equilibrium model rationalizes the evidence of Section 2 on the effects of

tariff cuts on product innovation and revenue productivity. We now extend it to general

equilibrium to analyze welfare. The set up is in Section 4.1 and the results are in Section

4.2. We model a small open economy with an exogenous set of firms. Appendix D.2

introduces free entry, and Appendix D.3 models two large and symmetric countries.27

25Pro-competitive effects on prices are larger for large firms also in Amiti et al. (2014) and Edmondet al. (2015).

26It is well known that revenue TFP captures efficiency and prices, and the literature has made progressin disentangling markups from efficiency gains. As Foster et al. (2008) explain, these methods apply tosectors with homogeneous goods, where TFPQ is meaningful. Harrison (1994), De Loecker (2007) andDe Loecker and Warzynski (2012) make similar points on changes in measured productivity during tradereforms. DeLoecker et al. (2016) propose a measurement that allows for vertically-differentiated goods,but maintain the other assumptions above.

27None of the results are affected by free entry. In the two-country model, the welfare results remainbut Proposition 7 may change. It assumes a large decrease in foreign costs a decrease in trade costs maynot be sufficient.

26

4.1 General Equilibrium Set Up

We describe Home, a small country that trades with large Foreign. Labor is the only input

into production. A representative household inelastically supplies its one unit of labor to

a perfect labor market. There is an exogenous continuum of sectors with measure one,

denoted with S ∈ [0, 1]. Each sector is modelled exactly as in Section 3 and we add sector

subscripts S to its variables. Sector S is endowed with a single nest of less-differentiated

varieties OS, and exogenous finite sets of Home and Foreign firms.

Foreign firms are partitioned into a less-differentiated set OFS and a differentiated

set DFS. Less-differentiated firms produce in the less-differentiated nest OFS ⊂ OS, and

each differentiated firm i ∈ DFS has its own nest. These sets are characterized by vectors

of unit costs {ci0S}i∈OFS and {ciDS}i∈OFS , which are bounded away from zero and are

continuous in S except for at most a finite set of sectors S in which the number of firms

in OFS or DFS change.

Home firm i ∈ S chooses to exit the Home market, to supply it with a less-differentiated

variety, or to supply it with a differentiated variety following the strategic game in Section

3. If the firm produces a less-differentiated variety, its fixed cost of production is f0 = wf0

and its unit cost is ci0S = wci0S. If the firm produces a differentiated variety, these costs

are respectively fD = wfD and ciDS = wciDS, where w is the wage rate, and ci0S, ciDS, f0,

and fD are exogenous labor requirements. Let mS be the number of Home firms in sector

S, and assume vectors (c10S, ..., cmS0S) and (c1DS, ..., cmSDS) are bounded away from zero

and are continuous in S except for at most a finite number of sectors where mS changes.

In addition to supplying Home, each Home firm i ∈ S may export to Foreign. If it

exports, it incurs a fixed cost f ∗ units of labor and gets the following sales and net profits

from exporting:

X∗(ci0S) = (wci0S)1−σY ∗, (9)

π∗(ci0S) =X∗(ci0S)

σ− wf ∗

where Y ∗ > 0 is a parameter. The firm exports if and only if ci0S ≤ c∗(w), where

c∗(w) = w−1(

Y ∗

σwf ∗

)1/(σ−1)

.

The assumption that domestic firms do not price strategically in Foreign is only for

simplicity. The key assumption is that a firm’s decisions to export and to differentiate

its product are independent. It is not implausible in our leading example of automobile

27

companies. Chery may provide variety and replacement parts in China, where it owns

many production facilities, but not in foreign countries through exports alone.28

Suppose all firms in all sectors play the unique subgame perfect equilibrium of Section

3 above given a vector of the wage rate, overall price index, and income (w,P , y). Denote

with OHS and DHS the equilibrium sets of less-differentiated and differentiated domestic

varieties respectively. The equilibrium set of less-differentiated varieties in sector S is

(OHS ∪ OFS) = OS, and of differentiated varieties is (DHS ∪ DFS) = DS. Then, the set

of all nests in (5) is N = {OS ∪ DS}S∈[0,1] and the price index is

P =

[∫ 1

0

[P0(c0S)]1−η +∑i∈DS

(ηciDSη − 1

)1−η

dS

]1/(1−η)(10)

where P0(c) is the equilibrium price index in a less-differentiated nest with a vector of unit

costs c, when firms price according to (7), and c0S is the vector of unit costs in nest OS in

the subgame perfect equilibrium. Given the assumptions on boundedness and continuity,

these prices P0(c0S) are continuous in S in all but a zero-measure set of sectors in which

OFS, DFS, OHS, or DHS change exogenously or endogenously through changes in Home

firms’ discrete choices. Hence, the integral is well defined and continuous in any (w,P , y).

Integrals in (11) and (12) below have the same properties for the same reasons.

The representative household gets income from labor and profits:

y = w +

∫ 1

0

∑{i∈S:ci0S≤c∗(w)}

π∗(ci0S) +∑i∈DHS

πD(ciDS) +∑i∈OHS

π0(c−i0S, ci0S)

dS (11)

Define PF0(c0FS, c0HS) as the price index of the less differentiated nest OS in (4)

where only foreign firms are included in the sum, when the vector of Foreign unit costs

is c0FS = {ci0S}i∈OFS and the vector of Home unit costs is c0HS = {ci0S}i∈OHS . Trade is

28The interdependence between decisions of exporting and product differentiation arises if there areeconomies of scale to producing the same variety for the domestic and foreign markets. Then trade, byexpanding the opportunities to export less-differentiated varieties, may decrease the incentives for firmsto differentiate. Also in foreign direct investment, the decision of servicing a foreign market throughexports or a foreign affiliate may be influenced by the affiliate’s ability to couple the firm’s products withnon-tradable services. While interesting, these cases are beyond the scope of this paper.

28

balanced if Home exports to Foreign equals its imports from Foreign:

Y ∗w1−σ∫ 1

0

∑{i∈S:ci0S≤c∗(w)}

(ci0S)1−σdS

= yPη−1∫ 1

0

[[PF0(c0FS, c0HS)]1−σ[P0(c0S)]σ−η +

∑i∈DFS

(ηciDSη − 1

)1−η]dS. (12)

The general equilibrium is a set of strategies, one for each firm, and a vector (w,P , y)

such that firm strategies are subgame perfect equilibrium strategies in all sectors, and

equations (10), (11) and (12) hold.29

4.2 Market Inefficiencies and Trade

We find conditions for trade to increase differentiation in general equilibrium, and evaluate

whether such differentiation improves welfare. We start by showing market inefficiencies

in the allocation of labor and in discrete choices. Throughout, denote the markup of firm

i ∈ OS with µi0S and the markup of i ∈ DS as µD = η/(η − 1). These markups are the

equilibrium markups for all subgames after discrete choices are made, not just for the

subgame perfect equilibrium path. Markup µi0S, implicitly defined in (7), depends on the

vector of all unit costs in OS but we omit its argument for ease of notation.

Lemma 5 Labor misallocation. Consider any set of discrete choices with the corre-

sponding profit-maximizing prices and market-clearing quantities. A planner can reallocate

labor used for domestic production but cannot change discrete choices or the quantities

imported and exported. For any two firms in the same nest, the planner allocates rela-

tively more labor to the more productive firm compared to the market. The planner also

allocates more labor to differentiated varieties relative to less-differentiated varieties.

As in the literature, markup dispersion leads to labor missallocation. The proof in

Appendix D is a small extension of Edmond et al. (2015). To see it, consider two less-

differentiated varieties i, i′ ∈ S with labor requirements ci0S < ci′0S and hence markups

µ0iS > µ0i′S. Standard CES maximization implies the following relationship between the

29Although the subgame perfect equilibrium is unique in all sectors for any (w,P , y), multiple generalequilibria may exist because spending on foreign varieties may not be increasing in domestic wageseverywhere. For some parameter values, a decrease in w may increase product differentiation and decreasedomestic sales by Home firms. The results below are phrased to hold in cases with multiple equilibria.

29

planner’s and the market’s labor allocations:

laborplanneri

laborplanneri′

=

(ci0Sci′0S

)−σ>

(ci0S/µ0iS

ci′0S/µ0i′S

)−σ=

labormarketi

labormarketi′

.

The consumer chooses quantities based on prices, and the planner does it based on costs.

Then, the consumer spends relatively less on varieties with higher markups, the differ-

entiated varieties and the more productive varieties within the less-differentiated nest as

stated in Lemma 5.

We now turn to discrete choices. Fix a sector and consider a subgame after all of

discrete choices are made. Prices and quantities are set by the market equilibrium. A

planner can change a single firm’s discrete choice, and the market again sets prices and

quantities to the new subgame equilibrium. We compare the marginal social gain from

this change in discrete choice to the firm’s private gain.

Such a comparison involves reallocating labor from the variety to the rest of the

economy. Once fixed costs are incurred, the economy exhibits constant returns to scale.

Then, the marginal cost of labor is C = wL/Q where Q is the standard aggregate quantity

under nested CES preferences, Q = y/P , and L is labor allocated for production30

L = 1−∫ 1

0

(∣∣OHS∣∣f0 +∣∣DHS∣∣fD +

∣∣{i ∈ SH : ci0S ≤ c∗(w)}∣∣f ∗) dS

where∣∣·∣∣ denotes the number of elements in a set. Define the average markup as µ = P/C,

price over marginal cost. By Roy’s identity, the valuation of a differentiated variety i ∈ Sfor a planner who cannot determine prices and quantities is:

uD(ciDS) = P−1∫ ∞µDciDS

qD(p′)dp′︸ ︷︷ ︸consumer surplus

−C−1fD (13)

where P−1

is the marginal utility of income, µDciDS is the firm’s equilibrium price, and

30Aggregate quantity is:

Q =

[∫NQ(η−1)/ηn dn

]η/(η−1)where Qn =

[∑i∈n

q(σ−1)/σi

] σσ−1

The expression C = L/Q holds also in an open economy because, net of fixed costs, international tradeis effectively a constant returns to scale technology that transforms domestic goods into imports.

30

(a) Differentiated Variety (b) Less-Differentiated Variety

Figure 3: Consumer surplus terms (CS) in equations (13) and (16)

qD(p′) = Pη−1

(p′)−η is the quantity demanded from a differentiated firm with price p′

in equation (3). Figure 3(a) illustrates the consumer-surplus term. Since qD(p′) has

a constant elasticity the consumer surplus term has closed form solution, µDπD(ciDS).

Substituting it in (13), we have

uD(ciDS) = P−1µDπD(ciDS)− C−1fD (14)

= C−1[(

µDµ

)πD(ciDS)− fD

]> C−1[πD(ciDS)− fD] (15)

where the inequality holds because µD > µ.31 The term in brackets is firm i’s private

profit from producing a differentiated variety.

For a less-differentiated domestic variety, define q0(p−i0S, p′) as the quantity demanded

of variety i when its price is p′ and all its competitors’ prices are at their subgame equi-

librium level, vector p−i0S, with elements pi′0S. From equation (3),

q0(p−i0S, p′) = P

η−1(

(p′)1−σ +∑

i′∈OS ,i′ 6=i

(pi′0S)1−σ

)σ−η1−σ

(p′)−σ

Since vector p−i0S is a function of the vector of costs (c−i0S, ci0S) the marginal contribution

31The inequality holds strictly because the markup from exporting is σ/(σ − 1). If the markup fromexporting were µD, then a non-zero mass of firms sharing a nest would also imply µD > µ.

31

of firm i to welfare is also a function of these costs. It satisfies

u0(c−i0S, ci0S) < P−1∫ ∞µi0Sci0S

q0(p−i0S, p′)︸ ︷︷ ︸

consumer surplus

−C−1f0 (16)

< P−1µi0Sπ0(c−i0S, ci0S)− C−1f0 for all µi0S < µD (17)

< C−1(π0(c−i0S, ci0S)− f0) if µi0S < µ (18)

The first inequality holds because the variety does not have a monopoly in nest OS by

assumption (at least one foreign firm is in OS ). When the variety is taken out of the mar-

ket, the consumer’s valuation of other varieties in OS increases.32 The second inequality

is illustrated in Figure 3(b). The dashed line illustrates the hypothetical demand curve

qi(p) = Ap−ε where ε is the elasticity of demand of the firm (defined in equation (7))

and constant A is defined by the intersection point, qi(µi0Sci0S) = q0(p−i0S, µi0Sci0S). The

consumer surplus term if demand were qi(p) would be∫ ∞µi0Sci0S

Ap−εdp =A(µi0Sci0S)−ε+1

ε− 1=µi0Sci0S[q0(p−i0S, µi0Sci0S)]

ε− 1= µi0Sπ0(c−i0S, ci0S)

The shaded area in the figure is strictly less than the area implied by this constant

elasticity function, because the elasticity of demand is higher than ε for all prices higher

than the equilibrium price. The terms in parenthesis in (15) and (18) are the firm’s

private net profits under differentiation and less-differentiation, resepcively. Together,

inequalities (15), (17) and (18) imply:

Lemma 6 Consider the marginal social benefit of changing a firm’s discrete choice when

the planner cannot set prices and quantities after discrete choices are made. The marginal

social benefit of a differentiated variety is always greater than the private gain, whether

the comparison is to exiting or to producing a less-differentiated variety. The marginal

social benefit of a less-differentiated variety is smaller than the private profit if the firm

is sufficiently less productive than its competitors so that µ0i < µ.

In partial equilibrium Proposition 3, a sufficiently large decrease in foreign costs in-

creases the gain from differentiation for surviving firms. In general equilibrium, the con-

ditions for this result are more stringent because the decrease in the overall price index

P discourages differentiation if differentiation requires an investment, fD > f0.

32The demand and price of these other varieties increase. So, by Roy’s identity, their valuation increases.

32

Proposition 7 A sufficiently large decrease in foreign costs in a share α ∈ (0, 1) of

sectors increases exit from the domestic market of firms in all sectors. Among surviving

firms, it increases product differentiation if fD ≤ f0. Welfare after the shock is higher

than in the equilibrium of an alternative subgame in which these surviving firms do not

differentiate their products and other firms maintain their discrete choices.

Appendix C2 proves that, even when the shock is not enough to drive out all Home firms

from the domestic market, a sufficiently large decrease in foreign costs in a non-zero mass

of sectors decreases the overall price index P/w and P−i0/w in the sectors directly affected

by the shock. Then, operating profits πD and π0 from domestic sales in (6) both decrease.

The ratio of profits is

πDπ0

=εi0Sη

(P0S

w

)η−σ (εi0S ci0Sεi0S − 1

)σ−1(ηciDSη − 1

)1−η

where we have omitted the arguments of functions π and P0S, and εi0S is the firm’s

endogenous elasticity of demand if it is less-differentiated. The ratio πD/π0 changes with

the shock only through the cost of firm i’s competitors relative to wages, P−i0/w. Then,

the shock increases πD/π0. The net gain from product differentiation is πD−π0−w(fD−f0). The increase in the ratio πD/π0 increases this gain. The decrease in levels πD and π0

decreases the gain if f0 < fD, increases it if f0 > fD and has no effect if f0 = fD.

For the welfare claim, consider the set of firms that change from producing a less

differentiated variety in OS to producing a differentiated variety in DS in a non-zero

mass of sectors S.33 From Lemma 6, the social planner benefits from moving these firms

from DS back to OS after the trade shock only if general equilibrium effects increase the

profitability of less-differentiated varieties. Appendix C.2 shows that this is only possible

if Home’s terms of trade decrease (a welfare loss) and labor moves from differentiated

varieties to less-differentiated varieties, which reduces welfare by Lemma 5.

Table 4 suggests the empirical relevance of the condition fD ≤ f0. In sectors that

experienced disproportionately large tariff cuts, firms all sizes, small and large, introduced

new goods and switched to more skill intensive sectors. The model can only rationalize

increases in product differentiation among small firms if such differentiation does not

require large fixed costs, i.e., fD − f0 ≈ 0. Then, by Proposition 7, import competition

33We rule out the possibility that other firms respond optimally to more firms entering the less-differentiated nest because the social planner may value differentiation of various varieties in a differentordering than the strategic game played by the market. So, shifting a variety from differentiation to nestOS may increase welfare if it leads another firm to differentiate or exit nest O, partially correcting foranother market distortion.

33

increases product differentiation in the general equilibrium model. The welfare gains from

trade are higher with the differentiation option than in a scenario where firms cannot

differentiate their products, as in standard models.

A back of the envelope calculation suggests that these new gains from trade may be

sizable. The coefficient on column (2) of Table 2 indicates that a one standard deviation

reduction in log output tariffs (around .5) is associated with an increase in new products

of 0.8 percentage points in total sales (multiplied by -0.0157). If we set η = 2 and σ = 10

the welfare gain from increasing the number of new differentiated products by 0.008 and

decreasing more substitutable products by the same share increases welfare by 0.7 percent,

a significant value relative to standard calculations of the welfare gains from trade.34

5 Extension of the Model: Input Suppliers

We add inputs to the model to interpret the empirical results on the indirect effects of

tariff cuts on import-competing firms’ input suppliers. The exercise further highlights the

differences between measured productivity and non-pecuniary firm outcomes, discussed in

Section 3.2. Since the focus is on positive predictions, we return to the partial equilibrium

model of Section 3 and omit all sector subscripts. The general equilibrium results remain

if the sector of material inputs modelled is sufficiently small, say relative to labor and

capital, to affect downstream costs.

We assume that less-differentiated upstream firms sell only to less-differentiated down-

stream firms. This assumption is made for simplicity, and Appendix E.1 proves the results

under the weaker assumption that less-differentiated downstream firms use intensively

less-differentiated inputs, relative to differentiated downstream firms. If product differen-

tiation involves broad quality upgrades, this assumption is justified with ample evidence

from the literature that higher-quality firms use intensively higher-quality inputs.35 Take

again the auto-maker Chery. Its increase in product scope was viable through just-in-time

inventory controls and investments in modern equipment, which produces higher-quality

parts in small batches. Quality improvements were in Chery’s own interest given its

new commitment to make replacement parts available. To be effective, all these improve-

34Using the definition of P in (3), the estimated decrease in price is P ≈ 1.0081/(1−η) ∗ 0.9921/(1−σ).The value η = 2 is between Edmond et al. (2015)’s estimate η = 1.28 and Broda and Weinstein (2006)’smedian elasticity of 5-digit SITC codes, estimated to 2.7. To get a sense magnitude for the standard gainfrom trade, assume absorption as 50% larger than GDP and the elasticity of trade with respect to tradecosts to be 5. Imports as a share of GDP increased from 14% to 28% in the period of our data, then thewelfare gain in Arkolakis et al. (2012) is (0.81/0.91)−1/5 − 1 = 2.2 percent.

35See Schott (2004) and Verhoogen (2008) for skill intensity, and Kugler and Verhoogen (2011), Manovaand Zhang (2012), and Fieler et al. (2018) for labor and material input usage.

34

ments in Chery—production in small batches, higher-quality parts, and efficient inventory

controls—have to be matched by mirror improvements in its input suppliers.

5.1 Set up with input suppliers

We present the set up here and the results in Section 5.2. The downstream sector is

modelled exactly as in Section 3, and the upstream sector (input suppliers) is modelled

symmetrically. We use subscript U to distinguish upstream variables from the down-

stream variables above. There is an exogenous finite set of potentially active downstream

firms and upstream firms. A strict subset of these firms are foreign. Foreign firms have

exogenous unit costs and do not make discrete choices. They have pre-assigned nests and

at least one downstream foreign firm is in the less-differentiated downstream nest O.

Each input supplier has monopoly rights over a unique input variety. It chooses to exit,

produce a less-differentiated variety, or produce a differentiated variety. If it produces, it

chooses its price. To focus on import competition, we assume that the upstream firms

modelled do not export or that their decision to export is independent from their decision

to differentiate their products. If the upstream firm i produces a less-differentiated variety,

it pays a fixed cost f0U and an additional cost ci0U for each unit produced. If it produces

a differentiated variety, its fixed cost is fDU and unit cost is ciDU .

Less-differentiated firms. Less-differentiated upstream firms only sell inputs for the

variable production costs of less-differentiated downstream firms.36 The unit cost of a

domestic, less-differentiated downstream firm i ∈ O is ci0 = c0/φi0 where φi0 is a firm-

specific productivity parameter and c0 is the cost of a bundle of inputs, common to all

less-differentiated downstream varieties. Let

c0 =

[∫NU

P 1−ηUnU

dnU

] 11−ηU

(19)

where PnU =

[∑i∈nU

(pi)1−σU

] 11−σU

, (20)

and pi is the price of variety i, nU is a nest of inputs, and NU is the exogenous set of

these nests, which may include labor, capital, and materials from other sectors. Let OUbe the endogenous set of less-differentiated upstream varieties, and P0U be its price index

defined in (20). Since there is a continuum of nests NU , equilibrium P0U does not affect

36The proof of proposition 8 holds almost unchanged if inputs are also used in fixed costs. Only theexpression for X0U in (24) changes.

35

c0. Appendix E.2 studies the model where upstream firms are sufficiently large to affect

c0.37 Assume σU > ηU > 1.

A less-differentiated upstream firm with unit cost c chooses price p to maximize oper-

ating profit

maxpX0Uc

ηU−10 (P0U)σU−ηUp−σU (p− c) (21)

where X0U is the equilibrium total spending on less-differentiated materials by domestic

downstream firms (below).

Analogous to the downstream pricing equation (7), the optimal markup of the up-

stream firm is εU/(εU − 1) where the endogenous elasticity of demand is a weighted

average between the within-nest elasticity σU and the across-nest elasticity ηU :

εU = σU(1− sU) + ηUsU (22)

and sU = (p/P0U)1−σ is the market share of the firm in nest OU . Equation (22) implicitly

defines prices in nest OU given a vector of costs c0U . Following the notation in the

downstream sector, we write ε0U(c−i0U , ci0U) as the elasticity of demand of an upstream

firm with unit cost ci0U facing competitors with units costs vector c−i0U , and P0U(c0U) as

the equilibrium price index, with c0U = {ci0U}i∈OU . Firm i’s operating profit is

π0U(c−i0U , ci0U , X0U) = X0UcηU−10

[P0U(c0U)]σU−ηU

ε0U(c−i0U , ci0U)

([ε0U(c−i0U , ci0U)]ci0Uε0U(c−i0U , ci0U)− 1

)1−σU(23)

From (7) and (8), spending on variable inputs by less-differentiated downstream firms

is

X0U(c0F , c0H) = yPη−1

[P0(c0)]σ−η

∑i∈OH

(ε0(c−i0, ci0)

ε0(c−i0, ci0)− 1

)−σ(ci0)

1−σ (24)

The vector of Home and Foreign unit costs cH0 = {ci0}i∈OH and cF0 = {ci0}i∈OF enter

differently because Foreign firms selling domestically do not buy inputs locally.

Differentiated firms. Like in the downstream sector, the price and profit of a differ-

entiated variety are exogenous. A differentiated input supplier with unit cost c charges

37Pricing decisions of upstream firms change because they internalize the effect of their prices on c0, andon prices, sales and spending on materials by downstream firms. The main conclusions below hold, exceptthat less-differentiated upstream firms may decrease their markups in response to import competitiondownstream. This effect, however, is small if the ratio of the upstream firm sales to the total cost ofdomestic less-differentiated downstream firms is small. See Appendix E.2 for a precise expression.

36

markup ηUηU−1

over marginal cost and gets profits

πDU(c) = c1−ηUYDU . (25)

Parameter YDU captures the size and tightness of the market, input costs, and potential

efficiency changes from product differentiation. Input costs of differentiated downstream

firms ciD are also exogenous.

Equilibrium with input suppliers. There is an exogenous finite set of domestic

and foreign upstream and downstream firms. Foreign firms do not make discrete choices.

At least one downstream foreign firm is less-differentiated. The cost of all varieties is

exogenous and known. Timing is as follows. (i) In ascending order of costs ci0U , all

domestic upstream firms make their discrete choices. (ii) In ascending order of costs ci0,

all domestic downstream firms make their discrete choices. (iii) All firms, upstream and

downstream, domestic and foreign, simultaneously set prices. (iv) Markets clear.

Discrete choices are set before prices so that firms cannot commit on prices to manip-

ulate discrete choices. The ordering of (i) and (ii) is not important. The simultaneous

setting of prices implies that a firm best responds to other firms’ equilibrium prices, and

that the pricing decisions above are correctly specified. The actions of a finite set of

upstream firms in one input nest, out of a continuum, do not change ci0 or ciD. Hence,

the subgame perfect equilibrium in Section 3 is unchanged. But the sales and the dis-

crete choices of downstream firms affects the profits of upstream less-differentiated firms

through spending on materials X0U in (24).

5.2 Characteristics of the Equilibrium with Input Suppliers

The game among upstream firms is solved by backward induction as in Section 3. A

vector of all firms’ discrete choices determine the sets of exiting, less-differentiated and

differentiated varieties, upstream and downstream. The corresponding payoffs are the

operating profits in (8), (23), and (25) minus fixed costs. Starting with the least productive

downstream firm, each firm effectively chooses among subgames when choosing whether to

exit, produce a less-differentiated variety or a differentiated variety. For the same reason

as before, the subgame perfect equilibrium is unique up to a perturbation of parameters.

As in Proposition 1, the first mover advantage of more productive firms implies that

there exist exit cutoffs, c and cU for downstream and upstream firms, as long as their

productivity can be ranked (ci0 < ci′0 if and only if ciD < ci′D, and ci0U < ci′0U if and only

if ciDU < ci′DU). Proposition 8 states how the subgame perfect equilibrium changes when

37

the costs of downstream foreign firms decrease sufficiently. It focuses on upstream firms

only because the effect of the shock on downstream firms in Proposition 3 is unchanged.

Proposition 8 Upstream Firms and Import Competition Downstream A suffi-

ciently large decrease in the cost of downstream foreign firms increases the exit of upstream

firms. Among surviving upstream firms, it increases product differentiation and markups.

Proof By Proposition 3, a sufficiently large decrease in downstream foreign costs strictly

decreases the sales of downstream firms that remain less differentiated, and it decreases

the set of less-differentiated downstream firms, through exit or product differentiation. As

a result, the absorption of less-differentiated material inputs X0U decreases. As foreign

costs go to zero, X0U also goes to zero, so that π0U decreases for all less-differentiated

upstream firms even if the firm becomes a monopolist in set OU . Then, ex ante less-

differentiated upstream firms exit or differentiate their products. Their prices in (22) are

affected by the shock only if the set of less-differentiated input suppliers change. Since

we have just proved that a sufficiently large decrease in downstream foreign costs shrinks

set OU , it increases markups of upstream firms that remain less-differentiated. �

The effect of import competition downstream in increasing exit and product differ-

entiation is the same for import-competing firms and their input providers. But the

effect on the markups of less-differentiated firms is the opposite. Market shares deter-

mine the markups in the model. While import competition decreases the market share

of import-competing downstream firms, it does not directly change the market share of

upstream firms. Less-differentiated input suppliers increase their markups if other ex ante

less-differentiated input suppliers exit or differentiate.

This difference arises because, for a downstream firm, product differentiation consists

of finding a market niche where it can insulate itself from import-competition, while for

an upstream firm, differentiation changes the firm’s customers due to the assumption that

differentiated downstream production is intensive in differentiated inputs.

We use Proposition 8 to interpret the coefficients on downstream tariffs in our empirical

specification (1), which capture the effect of tariff cuts on the input suppliers of import-

competing firms. Tables 2 and 3 suggest that, in response to tariff cuts downstream,

these input suppliers introduce new goods and switch to skill-intensive sectors, in line

with increases in product differentiation in the model. In all specifications, either the

coefficient on downstream tariffs is smaller (in magnitude) and less statistically significant

than the coefficient on output tariffs, or equality cannot be rejected. This result suggests

plausibly that the indirect effect of tariff cuts on input suppliers is smaller than the direct

effect on import-competing firms.

38

In contrast, when the dependent variable is TFP in Table 1, the coefficient on down-

stream tariffs is about seven times larger than the coefficient on output tariffs in all IV

specifications. This result is in line with the movement in markups predicted by Propo-

sition 8 and reinforces our earlier caution on interpreting TFP changes during trade

liberalizations (Section 3.2).

6 Robustness and Extensions of Empirical Results

We focus on robustness and extensions of the empirical results. References to the theo-

retical appendices appear in Sections 3 through 5. Appendix A.2 tests other predictions

of the model. Output and downstream tariff reductions increase the probability of exiting

(Table A.8) and of switching four-digit sectors (Table A.9). The latter result is indicative

that the firm changes its output in response to tariff cuts, as predicted by the model.

Appendix A.1 repeats the TFP regression of Table 1 for various specifications. Ta-

ble A.1 uses lagged tariffs and includes SOE’s and multinationals with minority foreign

ownership, in a specification close to Brandt et al. (2017).38 Table A.2 drops sector fixed

effects. To check if collinearity between tariff measures is driving the results, Table A.3

confirms that the coefficients do not change when we drop one tariff measure at a time

from the regressions. To check for selection, Table A.4 repeats the regression using a bal-

anced panel of the firms that are in the sample during all ten years of data. We also follow

Wooldridge (2010) in estimating a selection equation using a probit, and then including

the estimated Mills ratio in the main specification (Table A.5). In Table A.6, we exclude

from the regression data on key sectors like textiles and apparel, and the computer in-

dustry. Table A.6 includes tariffs in the first stage of the TFP estimation, and Table A.7

estimates TFP following Ackerberg et al. (2015).

In all IV specifications of Tables A.1 through A.7, the magnitude of the coefficient on

downstream tariffs is seven to ten times larger than the coefficient on output tariff. The

coefficient on output tariff is generally negative, but it is less robust, in terms of statistical

significance in the OLS and IV specifications, than the coefficient on downstream tariffs.

These results are consistent with the model where import competition has an ambiguous

effect on the revenue productivity of import-competing firms (Proposition 3) and increases

the productivity of these firms’ input suppliers (Proposition 8).

38In principle, our mechanism applies to multinationals operating in China. A difference arises if (i)domestic firms have better information about the Chinese market and an edge at tailoring their goodsto domestic tastes, or (ii) if multinational affiliates are oriented towards global production chains andforeign markets and are not as affected by import-competition in China.

39

In the TFP regressions of Table 4, the coefficient on output tariffs increases system-

atically with quartile of firm sales. The coefficient on the largest quartile is positive,

and the coefficient on the smallest quartile is negative, and the difference is statistically

significant. Appendix Table A.8 repeats the regression of Table 4 (i) including SOE’s

and multinationals (ii) with only a balanced panel of firms, (iii) with TFP measured a

la Ackerberg et al. (2015), (iv) excluding textiles and apparel, and (v) excluding com-

puters and peripherals. Table A.8 presents the results for all firms and for non-exporters

separately, for OLS and IV regressions, and where applicable, for estimating the TFP

regression (2) with the Olley-Pakes method or with OLS. The results in Table 4 hold in

all these specifications.

Tables 2 and 3 associate tariff cuts to the introduction of new goods and to switches

to more skill intensive sectors. Appendix Tables A.9 though A.12 modify the regressions

in Tables 2 and 3 by (i) including SOE’s and multinationals with minority foreign own-

ership (ii) including only a balanced panel of firms, (iii) excluding textiles and apparel,

and (iv) excluding computers and peripherals. Relative to Table 2, the results on the

introduction of new goods are weaker when we include SOE’s and multinationals (Table

A.9A) or when we include only a balanced panel of firms (Table A.9B). Multinationals

may be disadvantaged relative to local private firms to tailor their goods to the domestic

market or to offer non-tradable services. They may also be more influenced by offshoring

opportunities than import competition in China. The results may be weaker with the

balanced panel if surviving firms are more likely to have had very successful products and

be less prone to introduce new varieties. Reassuringly and in line with these explanations,

the coefficients are negative and statistically significant when we restrict the sample to

non-exporting firms, the set of firms for which we expect the results to hold more strongly.

Tables A.11 and A.12 confirm the finding in Table 3 that tariff cuts shift firms toward

skill-intensive sectors in China, an unskill-abundant country. In all specifications, the co-

efficients on output tariffs are negative and statistically significant, and they have roughly

the same magnitude as the coefficients in Table 3. In the IV regressions, the coefficients

on downstream tariffs are also negative, suggesting that input providers also shift to more

skill-intensive sectors in response to tariff cuts.

In sum, the Appendix confirms that, in response to tariff cuts, non-exporting domes-

tic firms introduce new products and shift toward skill-intensive sectors, consistent with

firms in the model escaping import competition through product differentiation. The

productivity regressions confirm that, when import competition tightens, the revenue

productivity of small firms increase relative to large firms, and that the revenue produc-

tivity of import-competing firms’ input suppliers increase. These movements in measured

40

productivity are consistent with the model’s predictions for markups.

7 Conclusion

We set out to narrow the gap between the academic literature and the prevailing view

among policy makers and economists that tariff cuts are good for the performance of

import-competing firms. We develop a simple extension of Atkeson and Burstein (2008),

where import-competing firms may differentiate their products to escape foreign com-

petition. In practice, firms may offer customized products, cater to domestic tastes, or

complement their products with non-tradable services. Since the increase in product dif-

ferentiation spurred by import competition improves welfare in the model, it provides a

rationale for policy makers’ view above.

Using data on Chinese firms during China’s accession to the WTO, we provide evidence

that import-competing firms respond to tariff cuts by introducing new goods, and switch-

ing to skill-intensive sectors. These findings suggest that import-competition encourages

product innovation, in line with the model and policy makers’ view. The ambiguous ef-

fect of import-competition on the markup of domestic firms in the model may explain the

mixed evidence in the literature relating tariff cuts to firm productivity. Through variable

markups, the model also explains more subtle effects of tariff cuts on the revenue pro-

ductivity of heterogeneous firms and input suppliers. Revenue productivity, the standard

measure of firm performance in the empirical literature, is a poor measure of product dif-

ferentiation because it confounds the positive effects of import competition on innovation

with negative pro-competitive effects on markups. We circumvent this difficulty using

data on non-pecuniary firm outcomes which are comparable across time even in periods

of large changes in demand, technologies and output, such as trade liberalization episodes.

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